document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831646>Question 831646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find sin theta if cos theta=1/2 and theta terminates in quadrant IV </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501550 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=501550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For angles terminating in quadrant IV, sine is negative and cosine is positive.<BR>\n" );
document.write( "For any angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29+%2B+cos%5E2%28theta%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+%2B+cos%5E2%28theta%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28theta%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29+%2B+%281%2F2%29%5E2=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+%2B+%281%2F2%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29+%2B+1%2F4=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+%2B+1%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29=1-1%2F4 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29=1-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29=3%2F4 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29%3E0 ALIGN=MIDDLE  ALT=\"sin%28theta%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=-sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29=-sqrt%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a solution.<BR>\n" );
document.write( "The solution is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29=sqrt%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sin%28theta%29=sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28sin%28theta%29=sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "We also know that one of the possible values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60%5Eo ALIGN=MIDDLE  ALT=\"-60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-pi%2F3 ALIGN=MIDDLE  ALT=\"-pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "because a 30-60-90 right triangle (one with angles measuring 30, 60, and 90 degrees) is half of an equilateral triangle><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.1%2C1.1%2C-0.6%2C0.6%2C%0D%0Atriangle%280%2C0%2C0.866%2C0.5%2C0.866%2C-0.5%29%2C%0D%0Agreen%28line%280%2C0%2C0.866%2C0%29%29%2C%0D%0Agreen%28rectangle%280.816%2C0%2C0.866%2C0.05%29%29%2C%0D%0Alocate%280.88%2C0.3%2C1%2F2%29%2Clocate%280.88%2C-0.2%2C1%2F2%29%2C%0D%0Alocate%280.44%2C0.25%2C1%29%2Clocate%280%2C44%2C-0.27%2C1%29%2C%0D%0Ared%28arc%280.866%2C0.5%2C0.3%2C0.3%2C90%2C150%29%29%2C%0D%0Alocate%280.72%2C0.38%2Cred%2860%5Eo%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So for an equilateral triangle with side length of 1,<BR>\n" );
document.write( "we get a right triangle where the leg opposite the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle (adjacent to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle) measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "meaning that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2830%5Eo%29=cos%2860%5Eo%29=1%2F2 ALIGN=MIDDLE  ALT=\"sin%2830%5Eo%29=cos%2860%5Eo%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );